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Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions

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Cited by:

  1. Bjarne Grimstad & Brage R. Knudsen, 2020. "Mathematical programming formulations for piecewise polynomial functions," Journal of Global Optimization, Springer, vol. 77(3), pages 455-486, July.
  2. Benjamin Beach & Robert Hildebrand & Joey Huchette, 2022. "Compact mixed-integer programming formulations in quadratic optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 869-912, December.
  3. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
  4. Liu, Haoxiang & Wang, David Z.W., 2015. "Global optimization method for network design problem with stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 20-39.
  5. Burer, Samuel & Piccialli, Veronica, 2019. "Three methods for robust grading," European Journal of Operational Research, Elsevier, vol. 272(1), pages 364-371.
  6. Li, Han-Lin & Fang, Shu-Cherng & Huang, Yao-Huei & Nie, Tiantian, 2016. "An enhanced logarithmic method for signomial programming with discrete variables," European Journal of Operational Research, Elsevier, vol. 255(3), pages 922-934.
  7. Silva, Thiago Lima & Camponogara, Eduardo, 2014. "A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization," European Journal of Operational Research, Elsevier, vol. 232(3), pages 630-642.
  8. Fortz, Bernard & Gouveia, Luís & Joyce-Moniz, Martim, 2017. "Models for the piecewise linear unsplittable multicommodity flow problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 30-42.
  9. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
  10. Ashayeri, Jalal & Ma, Ning & Sotirov, Renata, 2015. "The redesign of a warranty distribution network with recovery processes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 184-197.
  11. Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
  12. Lingxun Kong & Christos T. Maravelias, 2020. "On the Derivation of Continuous Piecewise Linear Approximating Functions," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 531-546, July.
  13. Andreas Bärmann & Alexander Martin & Oskar Schneider, 2021. "Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling," Transportation Science, INFORMS, vol. 55(3), pages 747-767, May.
  14. Jin, Xiaoyu & Liu, Benxi & Liao, Shengli & Cheng, Chuntian & Zhang, Yi & Zhao, Zhipeng & Lu, Jia, 2022. "Wasserstein metric-based two-stage distributionally robust optimization model for optimal daily peak shaving dispatch of cascade hydroplants under renewable energy uncertainties," Energy, Elsevier, vol. 260(C).
  15. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
  16. Pedro Castro & Ignacio Grossmann, 2014. "Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems," Journal of Global Optimization, Springer, vol. 59(2), pages 277-306, July.
  17. Jon Lee & Daphne Skipper & Emily Speakman & Luze Xu, 2023. "Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 1-35, January.
  18. Alexander J. Zolan & Michael S. Scioletti & David P. Morton & Alexandra M. Newman, 2021. "Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1300-1319, October.
  19. Chase Rainwater & Joseph Geunes & H. Edwin Romeijn, 2014. "Resource-Constrained Assignment Problems with Shared Resource Consumption and Flexible Demand," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 290-302, May.
  20. Fang Fang & Harihara Prasad Natarajan, 2020. "Sourcing and Procurement Cost Allocation in Multi‐Division Firms," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 767-787, March.
  21. Xiaolin Huang & Jun Xu & Shuning Wang, 2012. "Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 145-164, October.
  22. Andreas Bärmann & Robert Burlacu & Lukas Hager & Thomas Kleinert, 2023. "On piecewise linear approximations of bilinear terms: structural comparison of univariate and bivariate mixed-integer programming formulations," Journal of Global Optimization, Springer, vol. 85(4), pages 789-819, April.
  23. Liu, Haoxiang & Szeto, W.Y. & Long, Jiancheng, 2019. "Bike network design problem with a path-size logit-based equilibrium constraint: Formulation, global optimization, and matheuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 284-307.
  24. Andrzej J. Osiadacz & Niccolo Isoli, 2020. "Multi-Objective Optimization of Gas Pipeline Networks," Energies, MDPI, vol. 13(19), pages 1-19, October.
  25. Aalami, Soheila & Kattan, Lina, 2022. "Proportionally fair flow markets for transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 24-41.
  26. Camponogara, Eduardo & Oliveira, Mateus Dubiela & Aguiar, Marco Aurélio Schmitz de, 2015. "Scheduling pumpoff operations in onshore oilfields under electric-power constraints," European Journal of Operational Research, Elsevier, vol. 247(3), pages 945-956.
  27. Archetti, Claudia & Bertazzi, Luca & Grazia Speranza, M., 2014. "Polynomial cases of the economic lot sizing problem with cost discounts," European Journal of Operational Research, Elsevier, vol. 237(2), pages 519-527.
  28. Steffen Rebennack, 2016. "Computing tight bounds via piecewise linear functions through the example of circle cutting problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 3-57, August.
  29. Joey Huchette & Joey Huchette, 2019. "A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 793-820, August.
  30. Jin, Xiaoyu & Liu, Benxi & Liao, Shengli & Cheng, Chuntian & Yan, Zhiyu, 2022. "A Wasserstein metric-based distributionally robust optimization approach for reliable-economic equilibrium operation of hydro-wind-solar energy systems," Renewable Energy, Elsevier, vol. 196(C), pages 204-219.
  31. S. Göttlich & A. Potschka & C. Teuber, 2019. "A partial outer convexification approach to control transmission lines," Computational Optimization and Applications, Springer, vol. 72(2), pages 431-456, March.
  32. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.
  33. Liu, Weiwei & Kong, Nan & Wang, Mingzheng & Zhang, Lingling, 2021. "Sustainable multi-commodity capacitated facility location problem with complementarity demand functions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
  34. Toriello, Alejandro & Vielma, Juan Pablo, 2012. "Fitting piecewise linear continuous functions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 86-95.
  35. Mehrani, Saharnaz & Sefair, Jorge A., 2022. "Robust assortment optimization under sequential product unavailability," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1027-1043.
  36. Jin, Xiaoyu & Liu, Benxi & Liao, Shengli & Cheng, Chuntian & Jurasz, Jakub & Zhang, Yi & Lu, Jia, 2023. "Exploring the transition role of cascade hydropower in 100% decarbonized energy systems," Energy, Elsevier, vol. 279(C).
  37. Juan Pablo Vielma, 2018. "Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139," Management Science, INFORMS, vol. 64(10), pages 4721-4734, October.
  38. Nasini, Stefano & Labbé, Martine & Brotcorne, Luce, 2022. "Multi-market portfolio optimization with conditional value at risk," European Journal of Operational Research, Elsevier, vol. 300(1), pages 350-365.
  39. Shima Azizi & Cem Deniz Caglar Bozkir & Andrew C. Trapp & O. Erhun Kundakcioglu & Ali Kaan Kurbanzade, 2021. "Aid Allocation for Camp‐Based and Urban Refugees with Uncertain Demand and Replenishments," Production and Operations Management, Production and Operations Management Society, vol. 30(12), pages 4455-4474, December.
  40. Birolini, Sebastian & Antunes, António Pais & Cattaneo, Mattia & Malighetti, Paolo & Paleari, Stefano, 2021. "Integrated flight scheduling and fleet assignment with improved supply-demand interactions," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 162-180.
  41. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
  42. Birolini, Sebastian & Jacquillat, Alexandre & Cattaneo, Mattia & Antunes, António Pais, 2021. "Airline Network Planning: Mixed-integer non-convex optimization with demand–supply interactions," Transportation Research Part B: Methodological, Elsevier, vol. 154(C), pages 100-124.
  43. Böttger, T. & Grimm, V. & Kleinert, T. & Schmidt, M., 2022. "The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1095-1111.
  44. Kazda, Kody & Li, Xiang, 2024. "A linear programming approach to difference-of-convex piecewise linear approximation," European Journal of Operational Research, Elsevier, vol. 312(2), pages 493-511.
  45. Brian J. Lunday & Hanif D. Sherali & Theodore S. Glickman, 2010. "The Nested Event Tree Model with Application to Combating Terrorism," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 620-634, November.
  46. Er-Rahmadi, Btissam & Ma, Tiejun, 2022. "Data-driven mixed-Integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 337-353.
  47. Miten Mistry & Dimitrios Letsios & Gerhard Krennrich & Robert M. Lee & Ruth Misener, 2021. "Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1103-1119, July.
  48. Hua, Hao & Hovestadt, Ludger & Tang, Peng & Li, Biao, 2019. "Integer programming for urban design," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1125-1137.
  49. Qi An & Shu-Cherng Fang & Tiantian Nie & Shan Jiang, 2018. "$$\ell _1$$ ℓ 1 -Norm Based Central Point Analysis for Asymmetric Radial Data," Annals of Data Science, Springer, vol. 5(3), pages 469-486, September.
  50. Srikrishna Sridhar & Jeffrey Linderoth & James Luedtke, 2014. "Models and solution techniques for production planning problems with increasing byproducts," Journal of Global Optimization, Springer, vol. 59(2), pages 597-631, July.
  51. Liron Ravner & Yoni Nazarathy, 2017. "Scheduling for a processor sharing system with linear slowdown," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 71-102, August.
  52. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "A Note on “A Superior Representation Method for Piecewise Linear Functions”," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 493-497, August.
  53. Steffen Rebennack & Vitaliy Krasko, 2020. "Piecewise Linear Function Fitting via Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 507-530, April.
  54. Moritz Link & Stefan Volkwein, 2023. "Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs," Journal of Global Optimization, Springer, vol. 87(1), pages 97-132, September.
  55. Denis Sauré & Juan Pablo Vielma, 2019. "Ellipsoidal Methods for Adaptive Choice-Based Conjoint Analysis," Operations Research, INFORMS, vol. 67(2), pages 315-338, March.
  56. Dulebenets, Maxim A. & Ozguven, Eren Erman, 2017. "Vessel scheduling in liner shipping: Modeling transport of perishable assets," International Journal of Production Economics, Elsevier, vol. 184(C), pages 141-156.
  57. Kevin-Martin Aigner & Robert Burlacu & Frauke Liers & Alexander Martin, 2023. "Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 458-474, March.
  58. Scott Kolodziej & Pedro Castro & Ignacio Grossmann, 2013. "Global optimization of bilinear programs with a multiparametric disaggregation technique," Journal of Global Optimization, Springer, vol. 57(4), pages 1039-1063, December.
  59. Eduardo Rauh Müller & Eduardo Camponogara & Laio Oriel Seman & Eduardo Otte Hülse & Bruno Ferreira Vieira & Luis Kin Miyatake & Alex Furtado Teixeira, 2022. "Short-term steady-state production optimization of offshore oil platforms: wells with dual completion (gas-lift and ESP) and flow assurance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 152-180, April.
  60. Jin, Kun & Wang, Wei & Li, Xinran & Hua, Xuedong & Chen, Siyuan & Qin, Shaoyang, 2022. "Identifying the critical road combination in urban roads network under multiple disruption scenarios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
  61. Scott J. Davis & Shatiel B. Edwards & Gerald E. Teper & David G. Bassett & Michael J. McCarthy & Scott C. Johnson & Craig R. Lawton & Matthew J. Hoffman & Liliana Shelton & Stephen M. Henry & Darryl J, 2016. "Maximizing the U.S. Army’s Future Contribution to Global Security Using the Capability Portfolio Analysis Tool (CPAT)," Interfaces, INFORMS, vol. 46(1), pages 91-108, February.
  62. Ma, N., 2014. "Optimal scope of supply chain network & operations design," Other publications TiSEM e6187708-b664-44bf-aef8-f, Tilburg University, School of Economics and Management.
  63. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
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